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We derive the microwave bandwidth of ultrafast optoelectronic samplers based on photoconducting switches, using a simple analytical model. The validity of this model is checked by measuring the bandwidth of semi-intrinsic and low-temperature-grown GaAs photoswitches. The bandwidth of such devices is limited by the response time of both the semiconductor material and the electrical circuit. The devices behave as low-pass filters exhibiting a -60 dB/decade slope.